In known fuel metering apparatus, the amount of fuel to be metered to the internal combustion engine is controlled in dependence on operating characteristics such as load, rotational speed and/or temperature of the internal combustion engine. Further, it is known to extend these control systems such that quantities characteristic of the amount of fuel actually injected into the internal combustion engine are utilized for the control of the fuel metering apparatus. For this purpose, for example, a signal indicative of the position of the rack is formed and used as the characterizing quantity of the amount of fuel actually injected. Now it may happen that, as a result of age and/or other phenomena, this characterizing quantity no longer corresponds to the amount of fuel actually injected into the internal combustion engine. Thus the control system determining the amount of fuel to be metered may be disturbed, for example, as a result of: wear of the pump drive and/or the quantity controlling unit; changes of the rack position sensor; compressibility and/or viscosity of the fuel; and, temperature-dependent changes of one or several components of the fuel metering apparatus. Consequently, the fact that it is not the amount of fuel actually injected but instead only a quantity characteristic of this amount that is measured, and further that the exact relationship between these two quantities is not known at any time, are the reasons why fuel metering to the internal combustion engine may be subject to permanent errors.